Abstract:

Hazel, A. L., Heil, M., Waters, S.L. & Oliver, J.M. (2011) On the liquid lining in fluid-conveying curved tubes Journal of Fluid Mechanics (in press)

We consider axially uniform, two-phase flow through a rigid curved tube in which a fluid (air) core is surrounded by a film of a second, immiscible fluid (water): a simplified model for flow in a conducting airway of the lung. Jensen (J. Fluid Mech., 331, 1997, 373-403) showed that, in the absence of a core flow, surface tension drives the system towards a configuration in which the film thickness tends to zero on the inner wall of the bend. In the present work, we demonstrate that the presence of a core flow, driven by a steady axial pressure gradient, allows the existence of steady states in which the film thickness remains finite ,a consequence of the fact that the tangential stresses at the interface, imposed by secondary flows in the core, can oppose the surface-tension-driven flow. For sufficiently strong surface tension, the steady configurations are symmetric about the plane containing the tube's centreline, but as the surface tension decreases the symmetry is lost through a pitchfork bifurcation, which is closely followed by a limit point on the symmetric solution branch. This solution structure is found both in simulations of the Navier-Stokes equations and a thin-film model appropriate for weakly curved tubes. Analysis of the thin-film model reveals that the bifurcation structure arises from a perturbation of the translational degeneracy of the interface location in a straight tube.